I didn't get any answers to my previous question; so I am trying a different tack.
I am familiar with a first course in probability theory using measure theory, to the extent of proving the Central ...

I am a bit rusty on this.
So let us consider the following two dimensional standard Brownian motion issued from zero defined on the probability space $(\Omega, \mathcal{F},\mathbb{P})$ (note that, in ...

Here is the exercise I have been struggling to solve. It is taken from this book by Revuz and Yor: link. Here is the full text of the problem ( Exercise 3.32, chapter 4).
Exercise (3.32). Let $B$ and ...

Let $B$ be a standard Brownian motion on $(\Omega, \mathcal{F}, P, ({\mathcal{F}_t})_{t\ge0})$, where the filtration is the one generated by $B$. Fix a time interval $[0,T]$. Define the process $X$ as ...

Let $\{t_i\}_{i=1}^n$ be a partition of $[0,t]$ and $W$ a standard Brownian motion. Write $W_i$ for $W_{t_i}$.
Show
$$
\lim \sum W_{i} (W_{i+1}-W_i)=\frac12 W^2_t-\frac12 t
$$
where the limit is in ...

I want to compute the fourth moment of a standard Wiener process: $E[W_t^4]$. My solution is not equal to the one in my textbook but I don't understand where I am wrong. I started by applying Ito's ...

Wikipedia has separate articles on "Brownian motion" and "Wiener process" (http://en.wikipedia.org/wiki/Brownian_motion and http://en.wikipedia.org/wiki/Wiener_process ). I am not an expert, but that ...

Imagine first a disk that is mostly stationary, except for random ("thermal" if you like) "rotational fluctuations" around its axis (which is fixed). Something a bit like what's shown in the figure ...

I want to find the best predictor of $(B_3-B_2)(B_4-B_{\pi})$ given an observation of $B_1$
Where $B_t$ is brownian motion for time $t \geq 0$.
I am not sure how to approach this.
I know it will be ...